171742 ÷ 61 
We're looking to find how many times 61 goes into 171742.

On to step 1:
When dividing 1 by 61, we get 0 with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Take the next digit (7) from the dividend and append it to 1, then repeat: 17 / 61

Going ahead to step 2:
If we divide 17 by 61, we get 0 and a remainder of 17.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 17, we end up with 17.
Fetch the next digit (1) from the dividend, attach it to 17 and continue: 171 / 61

On to step 3:
When dividing 171 by 61, we get 2 with a remainder of 49.
The next digit of our result is 2. 
Result so far: 2.0
Deduct 122 from 171 and we're left with 49.
Fetch the next digit (7) from the dividend, attach it to 49 and continue: 497 / 61

Step 4:
497 divided by 61 is 8 with a remainder of 9.
Use 8 as the next digit of our solution. 
Result so far: 28.0
If we take 488 away from 497, we end up with 9.
Bring next digit (4) of the dividend behind the 9 and repeat the process: 94 / 61

Step 5:
61 can be fit into 94 1 times, resulting in a remainder of 33.
Record the quotient 1 as the next digit in the result. 
Result so far: 281.0
If we take 61 away from 94, we end up with 33.
Fetch the next digit (2) from the dividend, attach it to 33 and continue: 332 / 61

Let's proceed to step 6:
The number 61 fits into 332 5 times, leaving a remainder of 27.
Put 5 as the next digit of the answer. 
Result so far: 2815.0
If we take 305 away from 332, we end up with 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Step 7:
When dividing 270 by 61, we get 4 with a remainder of 26.
The next digit of our result is 4. 
Result so far: 2815.4
The remainder is 26 after subtracting 244 from 270.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Moving on to step 8:
61 goes into 260 4 times with a remainder of 16.
Put 4 as the next digit of the answer. 
Result so far: 2815.44
Deduct 244 from 260 and we're left with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

The final outcome is 2815.44, with a leftover of 0.016.